Second-order Inductive Inference: an axiomatic approach
Consider a predictor who ranks eventualities on the basis of past cases: for instance a search engine ranking webpages given past searches. Resampling past cases leads to different rankings and the extraction of deeper information. Yet a rich database, with sufficiently diverse rankings, is often beyond reach. Inexperience demands either "on the fly" learning-by-doing or prudence: the arrival of a novel case does not force (i) a revision of current rankings, (ii) dogmatism towards new rankings, or (iii) intransitivity. For this higher-order framework of inductive inference, we derive a suitably unique numerical representation of these rankings via a matrix on eventualities x cases and describe a robust test of prudence. Applications include: the success/failure of startups; the veracity of fake news; and novel conditions for the existence of a yield curve that is robustly arbitrage-free.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Teaching Transformers Causal Reasoning through Axiomatic Training
For text-based AI systems to interact in the real world, causal reasoning is an essential skill. Since active interventions are costly, we study to what extent a system can learn causal reasoning from symbolic demonstrat…
Inductive BiasSecond-Order Uncertainty Quantification: Variance-Based Measures
Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper p…
Decision MakingUncertainty QuantificationChoice functions based on sets of strict partial orders: an axiomatic characterisation
Methods for choosing from a set of options are often based on a strict partial order on these options, or on a set of such partial orders. I here provide a very general axiomatic characterisation for choice functions of …
An axiomatic approach to default risk and model uncertainty in rating systems
In this paper, we deal with an axiomatic approach to default risk. We introduce the notion of a default risk measure, which generalizes the classical probability of default (PD), and allows to incorporate model risk in v…
Axiomatic Explanations for Visual Search, Retrieval, and Similarity Learning
Visual search, recommendation, and contrastive similarity learning power technologies that impact billions of users worldwide. Modern model architectures can be complex and difficult to interpret, and there are several c…
counterfactualFairnessImage RetrievalImage Similarity Search+1